Abstract

We present an analytical description of the motion in the singular logarithmic potential of the form Φ = ln √x21/b2 + x22, a potential which plays an important role in the modelling of triaxial systems (such as elliptical galaxies) or bars in the centres of galaxy discs. In order to obtain information about the motion near the singularity, we resort to McGehee-type transformations and regularize the vector field. In the axis-symmetric case (b = 1), we offer a complete description of the global dynamics. In the non-axis-symmetric case (b < 1), we prove that all orbits, with the exception of a negligible set, are centrophobic and retrieve numerically partial aspects of the orbital structure.